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Lateral free separation, definition

If, for the purpose of comparison of substrate reactivities, we use the method of competitive reactions we are faced with the problem of whether the reactivities in a certain series of reactants (i.e. selectivities) should be characterized by the ratio of their rates measured separately [relations (12) and (13)], or whether they should be expressed by the rates measured during simultaneous transformation of two compounds which thus compete in adsorption for the free surface of the catalyst [relations (14) and (15)]. How these two definitions of reactivity may differ from one another will be shown later by the example of competitive hydrogenation of alkylphenols (Section IV.E, p. 42). This may also be demonstrated by the classical example of hydrogenation of aromatic hydrocarbons on Raney nickel (48). In this case, the constants obtained by separate measurements of reaction rates for individual compounds lead to the reactivity order which is different from the order found on the basis of factor S, determined by the method of competitive reactions (Table II). Other examples of the change of reactivity, which may even result in the selective reaction of a strongly adsorbed reactant in competitive reactions (49, 50) have already been discussed (see p. 12). [Pg.20]

The original definition of ELF was based on the same-spin pair density, i.e., considering the electron localization with respect to another electron of identical spin. The ELF formulation of Savin opened not only the possibility to apply ELF to the DFT using KS orbitals but also to take into account the total electron density. Savin did not express the equations explicitly for separate spin contributions (as this was obvious). Possibly this was the reason for Madsen et al. [58] and later also Melin and Fuentealba [42] to propose in 1999 and 2003, respectively, to use ELF and ELF for free radical systems and to state that it is possible to evaluate ELF separately for the and p densities (which of course is already given by the original ELF). Melin and Fuentealba correctly mentioned that the sum of the spin-dependent functions does not yield the total ELF (the possibilities on how to include both spins within total ELF for spin-polarized systems were analyzed in 1996 by Kohout and Savin [16]). [Pg.130]


See other pages where Lateral free separation, definition is mentioned: [Pg.87]    [Pg.310]    [Pg.267]    [Pg.239]    [Pg.72]    [Pg.208]    [Pg.160]    [Pg.333]    [Pg.46]    [Pg.1]    [Pg.23]    [Pg.9]    [Pg.416]    [Pg.47]   


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